Finite Group Databasebeta

← C2×C23×#2008 #19171036

Subgroups — C2×C23×#2008 #19171036

Order 5888.

2118 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C23×#575C211yesmaximal, characteristic, complemented
2C22×C23×AGL(1,ℤ/8)C211yesmaximal, characteristic, complemented
3C2×C23×#535C211yesmaximal, characteristic, complemented
4C2×C23×#421C211yesmaximal, characteristic, complemented
5C2×C23×#418C211yesmaximal, characteristic, complemented
6C2×C23×#410C211yesmaximal, characteristic, complemented
7C23×#2008C218yesmaximal, direct product factor
8C2×C23×#344C211yesmaximal, characteristic, complemented
9C22×#41×C23C2211yescharacteristic
10C22×#41×C23C2211yescharacteristic
11C23×D4×C23C2211yescharacteristic
12C23×#575—22no—
13C23×#575—22no—
14C23×#575—22no—
15C23×#575C2214yescomplemented
16C2×C23×#137—21no—
17C2×C23×#137—21no—
18C2×C23×AGL(1,ℤ/8)—22no—
19C2×C23×AGL(1,ℤ/8)—22no—
20C2×C23×AGL(1,ℤ/8)—22no—
21C2×C23×AGL(1,ℤ/8)—21no—
22C2×C23×AGL(1,ℤ/8)—21no—
23C2×C23×AGL(1,ℤ/8)—22no—
24C2×C23×AGL(1,ℤ/8)—22no—
25C2×C23×AGL(1,ℤ/8)C2214yescomplemented
26C2×C23×#135—22no—
27C22×SD16×C23—21no—
28C22×D8×C23—21no—
29C22×M16×C23C2211yescharacteristic
30C22×M16×C23C2211yescharacteristic
31C23×#535—22no—
32C23×#535—22no—
33C23×#535—22no—
34C23×#535C2214yescomplemented
35C2×C23×#127—21no—
36C2×C23×#124—21no—
37C2×C23×#121—22no—
38C2×C23×#120—22no—
39C2×C23×#117C2211yescharacteristic
40C2×C23×#117C2211yescharacteristic
41C23×#421—22no—
42C23×#421C2214yescomplemented
43C2×C23×#104—22no—
44C23×#418—22no—
45C23×#418C2214yescomplemented
46C2×C23×#102—22no—
47C23×#410—22no—
48C23×#410C2214yescomplemented
49C2×C23×#99—22no—
50C23×#344C2214yescomplemented
51C25×C23—21no—
52C2×#41×C23—21no—
53C2×#41×C23—21no—
54C2×#41×C23—21no—
55C2×#41×C23—21no—
56C2×#41×C23—21no—
57C2×#41×C23—21no—
58C2×#41×C23—21no—
59C2×#41×C23—21no—
60C2×#41×C23—21no—
61C2×#41×C23—21no—
62C2×#41×C23—21no—
63C2×#41×C23—21no—
64C2×#41×C23—21no—
65C2×#41×C23—21no—
66C2×#41×C23—21no—
67C2×#41×C23—21no—
68C2×#41×C23—21no—
69C2×#41×C23—21no—
70C2×#41×C23—21no—
71C2×#41×C23—21no—
72C2×#41×C23D412yes—
73C2×#41×C23D412yescomplemented
74C2×#41×C23C2312yes—
75C2×#41×C23C2312yes—
76C22×Q8×C23D411yescharacteristic
77C22×Q8×C23D411yescharacteristic, complemented
78C22×D4×C23—21no—
79C22×D4×C23—21no—
80C22×D4×C23—24no—
81C22×D4×C23—21no—
82C22×D4×C23—21no—
83C22×D4×C23—21no—
84C22×D4×C23—21no—
85C22×D4×C23—21no—
86C22×D4×C23—21no—
87C22×D4×C23—21no—
88C22×D4×C23—21no—
89C22×D4×C23—21no—
90C22×D4×C23—21no—
91C22×D4×C23—21no—
92C22×D4×C23D412yes—
93C22×D4×C23D412yes—
94C22×D4×C23D411yescharacteristic
95C22×D4×C23D411yescharacteristic, complemented
96C22×D4×C23C2312yes—
97C23×C4×C23—21no—
98C23×C4×C23—21no—
99C23×C4×C23C2311yescharacteristic
100C23×#137—24no—
101C23×#137—24no—
102C23×#137—24no—
103C23×#137—24no—
104C23×AGL(1,ℤ/8)—28no—
105C23×AGL(1,ℤ/8)—28no—
106C23×AGL(1,ℤ/8)—24no—
107C23×AGL(1,ℤ/8)—24no—
108C23×AGL(1,ℤ/8)—28no—
109C23×AGL(1,ℤ/8)—24no—
110C23×AGL(1,ℤ/8)—24no—
111C23×AGL(1,ℤ/8)—28no—
112C23×#135—28no—
113C23×#135—28no—
114C2×Q16×C23—22no—
115C2×SD16×C23—24no—
116C2×SD16×C23—24no—
117C2×SD16×C23—22no—
118C2×SD16×C23—22no—
119C2×SD16×C23—24no—
120C2×D8×C23—24no—
121C2×D8×C23—24no—
122C2×D8×C23—22no—
123C2×D8×C23—24no—
124C2×M16×C23—21no—
125C2×M16×C23—21no—
126C2×M16×C23—21no—
127C2×M16×C23—21no—
128C2×M16×C23—21no—
129C2×M16×C23—21no—
130C2×M16×C23—21no—
131C2×M16×C23D412yescomplemented
132C2×M16×C23D412yescomplemented
133C2×M16×C23D412yescomplemented
134C2×M16×C23C2312yes—
135C2×M16×C23C2312yes—
136C22×C8×C23—21no—
137C22×C8×C23D412yescomplemented
138C23×#127—24no—
139C23×#127—24no—
140C23×#124—24no—
141C23×#124—24no—
142C23×#121—28no—
143C23×#121—28no—
144C23×#120—28no—
145C23×#120—28no—
146C23×#117—21no—
147C23×#117—21no—
148C23×#117—21no—
149C23×#117—21no—
150C23×#117—21no—
151C23×#117D412yes—
152C23×#117C2312yes—
153C23×#117C2312yes—
154C2×C4⋊C4×C23—21no—
155C2×C4⋊C4×C23—21no—
156C2×C22⋊C4×C23—24no—
157C2×C22⋊C4×C23—21no—
158C2×C22⋊C4×C23D412yes—
159C2×C42×C23—21no—
160C2×C42×C23—21no—
161C23×#104—28no—
162C23×#102—28no—
163C23×#99—28no—
164C24×C23—22no—
165C24×C23—21no—
166C24×C23—22no—
167C24×C23—21no—
168C24×C23—22no—
169C24×C23—41no—
170C24×C23—41no—
171C24×C23—41no—
172C24×C23—41no—
173C24×C23—84no—
174C24×C23C2×D411yescharacteristic
175#41×C23—22no—
176#41×C23—22no—
177#41×C23—22no—
178#41×C23—22no—
179#41×C23—22no—
180#41×C23—22no—
181#41×C23—22no—
182#41×C23—22no—
183#41×C23—22no—
184#41×C23—22no—
185#41×C23—22no—
186#41×C23—22no—
187#41×C23—22no—
188#41×C23—22no—
189#41×C23—22no—
190#41×C23—22no—
191#41×C23—41no—
192#41×C23—41no—
193#41×C23—41no—
194#41×C23—41no—
195#41×C23—41no—
196#41×C23—41no—
197#41×C23—41no—
198#41×C23—41no—
199#41×C23—41no—
200#41×C23—41no—
201#41×C23—41no—
202#41×C23—41no—
203#41×C23—41no—
204#41×C23—41no—
205#41×C23—41no—
206#41×C23—41no—
207C2×Q8×C23—21no—
208C2×Q8×C23—21no—
209C2×Q8×C23—21no—
210C2×Q8×C23—21no—
211C2×Q8×C23—21no—
212C2×Q8×C23—21no—
213C2×Q8×C23—21no—
214C2×Q8×C23—21no—
215C2×Q8×C23—21no—
216C2×Q8×C23—21no—
217C2×Q8×C23C2×D412yes—
218C2×Q8×C23C2×D412yescomplemented
219C2×D4×C23—22no—
220C2×D4×C23—22no—
221C2×D4×C23—22no—
222C2×D4×C23—22no—
223C2×D4×C23—216no—
224C2×D4×C23—21no—
225C2×D4×C23—21no—
226C2×D4×C23—22no—
227C2×D4×C23—22no—
228C2×D4×C23—21no—
229C2×D4×C23—21no—
230C2×D4×C23—22no—
231C2×D4×C23—22no—
232C2×D4×C23—21no—
233C2×D4×C23—21no—
234C2×D4×C23—22no—
235C2×D4×C23—22no—
236C2×D4×C23—21no—
237C2×D4×C23—22no—
238C2×D4×C23—22no—
239C2×D4×C23—22no—
240C2×D4×C23—22no—
241C2×D4×C23—21no—
242C2×D4×C23—21no—
243C2×D4×C23—21no—
244C2×D4×C23—22no—
245C2×D4×C23—22no—
246C2×D4×C23—22no—
247C2×D4×C23—22no—
248C2×D4×C23—22no—
249C2×D4×C23—41no—
250C2×D4×C23—41no—
251C2×D4×C23—41no—
252C2×D4×C23—41no—
253C2×D4×C23—41no—
254C2×D4×C23—41no—
255C2×D4×C23—41no—
256C2×D4×C23—41no—
257C2×D4×C23—41no—
258C2×D4×C23—41no—
259C2×D4×C23—41no—
260C2×D4×C23—41no—
261C2×D4×C23—41no—
262C2×D4×C23—41no—
263C2×D4×C23—41no—
264C2×D4×C23—41no—
265C2×D4×C23—41no—
266C2×D4×C23—41no—
267C2×D4×C23—41no—
268C2×D4×C23—41no—
269C2×D4×C23—88no—
270C2×D4×C23C2×D414yes—
271C2×D4×C23C2×D412yes—
272C2×D4×C23C2×D412yescomplemented
273C22×C4×C23—22no—
274C22×C4×C23—21no—
275C22×C4×C23—21no—
276C22×C4×C23—22no—
277C22×C4×C23—22no—
278C22×C4×C23—22no—
279C22×C4×C23—22no—
280C22×C4×C23—41no—
281C22×C4×C23—41no—
282C22×C4×C23—41no—
283C22×C4×C23—41no—
284C22×C4×C23—41no—
285C22×C4×C23—41no—
286C22×C4×C23—41no—
287C22×C4×C23—41no—
288C22×C4×C23—41no—
289C22×C4×C23C2×D411yescharacteristic
290C22×C4×C23C2×D411yescharacteristic
291C22×C4×C23C2×D411yescharacteristic
292C22×C4×C23C2×D411yescharacteristic
293C22×C4×C23C2×D411yescharacteristic
294C22×C4×C23C2×D411yescharacteristic
295C22×C4×C23C2×D411yescharacteristic
296C22×C4×C23C2×D411yescharacteristic
297C22×C4×C23C2×D411yescharacteristic
298C22×C4×C23C2×D411yescharacteristic
299C22×C4×C23C2×D411yescharacteristic
300C22×C4×C23#4111yescharacteristic
301C22×C4×C23#4111yescharacteristic
302C22×C4×C23C2411yescharacteristic
303Q16×C23—28no—
304SD16×C23—216no—
305SD16×C23—28no—
306SD16×C23—28no—
307D8×C23—216no—
308D8×C23—28no—
309M16×C23—22no—
310M16×C23—22no—
311M16×C23—22no—
312M16×C23—22no—
313M16×C23—22no—
314M16×C23—22no—
315M16×C23—22no—
316M16×C23C2×D414yescomplemented
317C2×C8×C23—22no—
318C2×C8×C23—22no—
319C2×C8×C23—22no—
320C2×C8×C23—22no—
321C2×C8×C23—22no—
322C2×C8×C23C2×D414yescomplemented
323C4⋊C4×C23—22no—
324C4⋊C4×C23—22no—
325C4⋊C4×C23—22no—
326C4⋊C4×C23—41no—
327C22⋊C4×C23—216no—
328C22⋊C4×C23—22no—
329C22⋊C4×C23—22no—
330C22⋊C4×C23—41no—
331C22⋊C4×C23C2×D414yes—
332C42×C23—22no—
333C42×C23—22no—
334C42×C23—22no—
335C42×C23—41no—
336C2×#2008C2311yesmaximal, characteristic, direct product factor, Sylow
337C23×C23—24no—
338C23×C23—22no—
339C23×C23—22no—
340C23×C23—42no—
341C23×C23—44no—
342C23×C23—48no—
343C23×C23—42no—
344C23×C23—42no—
345C23×C23—41no—
346C23×C23—41no—
347C23×C23—42no—
348C23×C23—42no—
349C23×C23—42no—
350C23×C23—41no—
351C23×C23—41no—
352C23×C23—42no—
353C23×C23—82no—
354C23×C23—84no—
355C23×C23—84no—
356C23×C23—84no—
357C23×C23—84no—
358C23×C23—84no—
359C23×C23—84no—
360C23×C23#12011yescharacteristic
361C23×C23#12011yescharacteristic
362C23×C23#12111yescharacteristic
363C23×C23#12111yescharacteristic
364C23×C23#12711yescharacteristic
365C23×C23#12711yescharacteristic
366C23×C23C22×D411yescharacteristic
367Q8×C23—22no—
368Q8×C23—22no—
369Q8×C23—22no—
370Q8×C23—22no—
371Q8×C23—41no—
372Q8×C23—41no—
373Q8×C23—41no—
374Q8×C23—41no—
375D4×C23—22no—
376D4×C23—24no—
377D4×C23—22no—
378D4×C23—22no—
379D4×C23—24no—
380D4×C23—22no—
381D4×C23—42no—
382D4×C23—42no—
383D4×C23—42no—
384D4×C23—42no—
385D4×C23—42no—
386D4×C23—42no—
387D4×C23—42no—
388D4×C23—42no—
389D4×C23—42no—
390D4×C23—42no—
391D4×C23—42no—
392D4×C23—42no—
393D4×C23—42no—
394D4×C23—42no—
395D4×C23—41no—
396D4×C23—41no—
397D4×C23—41no—
398D4×C23—41no—
399D4×C23—816no—
400C2×C4×C23—24no—
401C2×C4×C23—22no—
402C2×C4×C23—22no—
403C2×C4×C23—44no—
404C2×C4×C23—41no—
405C2×C4×C23—41no—
406C2×C4×C23—41no—
407C2×C4×C23—41no—
408C2×C4×C23—42no—
409C2×C4×C23—42no—
410C2×C4×C23—42no—
411C2×C4×C23—42no—
412C2×C4×C23—42no—
413C2×C4×C23—42no—
414C2×C4×C23—42no—
415C2×C4×C23—42no—
416C2×C4×C23—42no—
417C2×C4×C23—82no—
418C2×C4×C23#12011yescharacteristic
419C2×C4×C23#12011yescharacteristic
420C2×C4×C23#12011yescharacteristic
421C2×C4×C23#12011yescharacteristic
422C2×C4×C23#12011yescharacteristic
423C2×C4×C23#12011yescharacteristic
424C2×C4×C23#12011yescharacteristic
425C2×C4×C23#12011yescharacteristic
426C2×C4×C23#12011yescharacteristic
427C2×C4×C23#12011yescharacteristic
428C2×C4×C23#12111yescharacteristic
429C2×C4×C23#12111yescharacteristic
430C2×C4×C23#12111yescharacteristic
431C2×C4×C23#12111yescharacteristic
432C2×C4×C23#12111yescharacteristic
433C2×C4×C23#12111yescharacteristic
434C2×C4×C23#12111yescharacteristic
435C2×C4×C23#12111yescharacteristic
436C2×C4×C23#12111yescharacteristic
437C2×C4×C23#12111yescharacteristic
438C2×C4×C23#12711yescharacteristic
439C2×C4×C23#12711yescharacteristic
440C2×C4×C23C22×D411yescharacteristic
441C2×C4×C23C22×D411yescharacteristic
442C2×C4×C23C22×D411yescharacteristic
443C2×C4×C23C22×D411yescharacteristic
444C2×C4×C23C22×D411yescharacteristic
445C2×C4×C23C2×#4111yescharacteristic
446C8×C23—24no—
447C8×C23—24no—
448C2×#575C2×C2311yescharacteristic, complemented
449C22×AGL(1,ℤ/8)C2×C2311yescharacteristic, complemented
450C2×#535C2×C2311yescharacteristic, complemented
451C2×#421C2×C2311yescharacteristic, complemented
452C2×#418C2×C2311yescharacteristic, complemented
453C2×#410C2×C2311yescharacteristic, complemented
454#2008C2×C2318yesdirect product factor
455C2×#344C2×C2311yescharacteristic, complemented
456C22×C23—22no—
457C22×C23—22no—
458C22×C23—22no—
459C22×C23—41no—
460C22×C23—41no—
461C22×C23—41no—
462C22×C23—41no—
463C22×C23—44no—
464C22×C23—48no—
465C22×C23—42no—
466C22×C23—42no—
467C22×C23—44no—
468C22×C23—82no—
469C22×C23—82no—
470C22×C23—84no—
471C22×C23—82no—
472C22×C23—84no—
473C22×C23—84no—
474C22×C23—84no—
475C22×C23—84no—
476C22×C23—82no—
477C22×C23—84no—
478C22×C23—82no—
479C22×C23#39211yescharacteristic
480C22×C23#39211yescharacteristic
481C22×C23#39211yescharacteristic
482C22×C23#39211yescharacteristic
483C22×C23C2×#12011yescharacteristic
484C22×C23C2×#12111yescharacteristic
485C22×C23C2×#12711yescharacteristic
486C4×C23—44no—
487C4×C23—42no—
488C4×C23—42no—
489C4×C23—82no—
490C4×C23#39211yescharacteristic
491C4×C23#39211yescharacteristic
492C4×C23#39211yescharacteristic
493C4×C23#39211yescharacteristic
494C4×C23C2×#12011yescharacteristic
495C4×C23C2×#12011yescharacteristic
496C4×C23C2×#12111yescharacteristic
497C4×C23C2×#12111yescharacteristic
498C22×#41C22×C2311yescharacteristic
499C22×#41C22×C2311yescharacteristic
500C23×D4C22×C2311yescharacteristic
501#575—22no—
502#575—22no—
503#575—22no—
504#575C22×C2314yescomplemented
505C2×#137—21no—
506C2×#137—21no—
507C2×AGL(1,ℤ/8)—22no—
508C2×AGL(1,ℤ/8)—22no—
509C2×AGL(1,ℤ/8)—22no—
510C2×AGL(1,ℤ/8)—21no—
511C2×AGL(1,ℤ/8)—21no—
512C2×AGL(1,ℤ/8)—22no—
513C2×AGL(1,ℤ/8)—22no—
514C2×AGL(1,ℤ/8)C22×C2314yescomplemented
515C2×#135—22no—
516C22×SD16—21no—
517C22×D8—21no—
518C22×M16C22×C2311yescharacteristic
519C22×M16C22×C2311yescharacteristic
520#535—22no—
521#535—22no—
522#535—22no—
523#535C22×C2314yescomplemented
524C2×#127—21no—
525C2×#124—21no—
526C2×#121—22no—
527C2×#120—22no—
528C2×#117C22×C2311yescharacteristic
529C2×#117C22×C2311yescharacteristic
530#421—22no—
531#421C22×C2314yescomplemented
532C2×#104—22no—
533#418—22no—
534#418C22×C2314yescomplemented
535C2×#102—22no—
536#410—22no—
537#410C22×C2314yescomplemented
538C2×#99—22no—
539#344C22×C2314yescomplemented
540C2×C23—21no—
541C2×C23—21no—
542C2×C23—21no—
543C2×C23—21no—
544C2×C23—21no—
545C2×C23—21no—
546C2×C23—82no—
547C2×C23—84no—
548C2×C23—82no—
549C2×C23#200812yesdirect product factor
550C2×C23C2×#39211yescharacteristic
551C25—21no—
552C2×#41—21no—
553C2×#41—21no—
554C2×#41—21no—
555C2×#41—21no—
556C2×#41—21no—
557C2×#41—21no—
558C2×#41—21no—
559C2×#41—21no—
560C2×#41—21no—
561C2×#41—21no—
562C2×#41—21no—
563C2×#41—21no—
564C2×#41—21no—
565C2×#41—21no—
566C2×#41—21no—
567C2×#41—21no—
568C2×#41—21no—
569C2×#41—21no—
570C2×#41—21no—
571C2×#41—21no—
572C2×#41D4×C2312yes—
573C2×#41D4×C2312yescomplemented
574C2×#41C23×C2312yes—
575C2×#41C23×C2312yes—
576C22×Q8D4×C2311yescharacteristic
577C22×Q8D4×C2311yescharacteristic, complemented
578C22×D4—21no—
579C22×D4—21no—
580C22×D4—24no—
581C22×D4—21no—
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4—21no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4D4×C2312yes—
593C22×D4D4×C2311yescharacteristic
594C22×D4D4×C2312yes—
595C22×D4D4×C2311yescharacteristic, complemented
596C22×D4C23×C2312yes—
597C23×C4—21no—
598C23×C4—21no—
599C23×C4C23×C2311yescharacteristic
600#137—24no—
601#137—24no—
602#137—24no—
603#137—24no—
604AGL(1,ℤ/8)—28no—
605AGL(1,ℤ/8)—28no—
606AGL(1,ℤ/8)—24no—
607AGL(1,ℤ/8)—24no—
608AGL(1,ℤ/8)—28no—
609AGL(1,ℤ/8)—24no—
610AGL(1,ℤ/8)—24no—
611AGL(1,ℤ/8)—28no—
612#135—28no—
613#135—28no—
614C2×Q16—22no—
615C2×SD16—24no—
616C2×SD16—24no—
617C2×SD16—22no—
618C2×SD16—22no—
619C2×SD16—24no—
620C2×D8—24no—
621C2×D8—24no—
622C2×D8—22no—
623C2×D8—24no—
624C2×M16—21no—
625C2×M16—21no—
626C2×M16—21no—
627C2×M16—21no—
628C2×M16—21no—
629C2×M16—21no—
630C2×M16—21no—
631C2×M16D4×C2312yescomplemented
632C2×M16D4×C2312yescomplemented
633C2×M16D4×C2312yescomplemented
634C2×M16C23×C2312yes—
635C2×M16C23×C2312yes—
636C22×C8—21no—
637C22×C8D4×C2312yescomplemented
638#127—24no—
639#127—24no—
640#124—24no—
641#124—24no—
642#121—28no—
643#121—28no—
644#120—28no—
645#120—28no—
646#117—21no—
647#117—21no—
648#117—21no—
649#117—21no—
650#117—21no—
651#117D4×C2312yes—
652#117C23×C2312yes—
653#117C23×C2312yes—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C22⋊C4—24no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4D4×C2312yes—
659C2×C42—21no—
660C2×C42—21no—
661#104—28no—
662#102—28no—
663#99—28no—
664C23C2×#200811yescharacteristic, direct product factor, Sylow
665C24—22no—
666C24—21no—
667C24—22no—
668C24—21no—
669C24—22no—
670C24—41no—
671C24—41no—
672C24—41no—
673C24—41no—
674C24—84no—
675C24C2×D4×C2311yescharacteristic
676#41—22no—
677#41—22no—
678#41—22no—
679#41—22no—
680#41—22no—
681#41—22no—
682#41—22no—
683#41—22no—
684#41—22no—
685#41—22no—
686#41—22no—
687#41—22no—
688#41—22no—
689#41—22no—
690#41—22no—
691#41—22no—
692#41—41no—
693#41—41no—
694#41—41no—
695#41—41no—
696#41—41no—
697#41—41no—
698#41—41no—
699#41—41no—
700#41—41no—
701#41—41no—
702#41—41no—
703#41—41no—
704#41—41no—
705#41—41no—
706#41—41no—
707#41—41no—
708C2×Q8—21no—
709C2×Q8—21no—
710C2×Q8—21no—
711C2×Q8—21no—
712C2×Q8—21no—
713C2×Q8—21no—
714C2×Q8—21no—
715C2×Q8—21no—
716C2×Q8—21no—
717C2×Q8—21no—
718C2×Q8C2×D4×C2312yes—
719C2×Q8C2×D4×C2312yescomplemented
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—22no—
724C2×D4—216no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—22no—
728C2×D4—22no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—21no—
738C2×D4—22no—
739C2×D4—22no—
740C2×D4—22no—
741C2×D4—22no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—22no—
746C2×D4—22no—
747C2×D4—22no—
748C2×D4—22no—
749C2×D4—22no—
750C2×D4—41no—
751C2×D4—41no—
752C2×D4—41no—
753C2×D4—41no—
754C2×D4—41no—
755C2×D4—41no—
756C2×D4—41no—
757C2×D4—41no—
758C2×D4—41no—
759C2×D4—41no—
760C2×D4—41no—
761C2×D4—41no—
762C2×D4—41no—
763C2×D4—41no—
764C2×D4—41no—
765C2×D4—41no—
766C2×D4—41no—
767C2×D4—41no—
768C2×D4—41no—
769C2×D4—41no—
770C2×D4—88no—
771C2×D4C2×D4×C2314yes—
772C2×D4C2×D4×C2312yes—
773C2×D4C2×D4×C2312yescomplemented
774C22×C4—22no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—41no—
782C22×C4—41no—
783C22×C4—41no—
784C22×C4—41no—
785C22×C4—41no—
786C22×C4—41no—
787C22×C4—41no—
788C22×C4—41no—
789C22×C4—41no—
790C22×C4C2×D4×C2311yescharacteristic
791C22×C4C2×D4×C2311yescharacteristic
792C22×C4C2×D4×C2311yescharacteristic
793C22×C4C2×D4×C2311yescharacteristic
794C22×C4C2×D4×C2311yescharacteristic
795C22×C4C2×D4×C2311yescharacteristic
796C22×C4C2×D4×C2311yescharacteristic
797C22×C4C2×D4×C2311yescharacteristic
798C22×C4C2×D4×C2311yescharacteristic
799C22×C4C2×D4×C2311yescharacteristic
800C22×C4C2×D4×C2311yescharacteristic
801C22×C4#41×C2311yescharacteristic
802C22×C4#41×C2311yescharacteristic
803C22×C4C24×C2311yescharacteristic
804Q16—28no—
805SD16—216no—
806SD16—28no—
807SD16—28no—
808D8—216no—
809D8—28no—
810M16—22no—
811M16—22no—
812M16—22no—
813M16—22no—
814M16—22no—
815M16—22no—
816M16—22no—
817M16C2×D4×C2314yescomplemented
818C2×C8—22no—
819C2×C8—22no—
820C2×C8—22no—
821C2×C8—22no—
822C2×C8—22no—
823C2×C8C2×D4×C2314yescomplemented
824C4⋊C4—22no—
825C4⋊C4—22no—
826C4⋊C4—22no—
827C4⋊C4—41no—
828C22⋊C4—216no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—41no—
832C22⋊C4C2×D4×C2314yes—
833C42—22no—
834C42—22no—
835C42—22no—
836C42—41no—
837C23—24no—
838C23—22no—
839C23—22no—
840C23—42no—
841C23—44no—
842C23—48no—
843C23—41no—
844C23—41no—
845C23—41no—
846C23—41no—
847C23—42no—
848C23—42no—
849C23—42no—
850C23—42no—
851C23—42no—
852C23—42no—
853C23—82no—
854C23—84no—
855C23—84no—
856C23—84no—
857C23—84no—
858C23—84no—
859C23—84no—
860C23C23×#12011yescharacteristic
861C23C23×#12011yescharacteristic
862C23C23×#12111yescharacteristic
863C23C23×#12111yescharacteristic
864C23C23×#12711yescharacteristic
865C23C23×#12711yescharacteristic
866C23C22×D4×C2311yescharacteristic
867Q8—22no—
868Q8—22no—
869Q8—22no—
870Q8—22no—
871Q8—41no—
872Q8—41no—
873Q8—41no—
874Q8—41no—
875D4—22no—
876D4—24no—
877D4—22no—
878D4—22no—
879D4—24no—
880D4—22no—
881D4—42no—
882D4—42no—
883D4—42no—
884D4—42no—
885D4—42no—
886D4—42no—
887D4—42no—
888D4—42no—
889D4—42no—
890D4—42no—
891D4—42no—
892D4—42no—
893D4—41no—
894D4—41no—
895D4—41no—
896D4—41no—
897D4—42no—
898D4—42no—
899D4—816no—
900C2×C4—24no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—44no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—42no—
909C2×C4—42no—
910C2×C4—42no—
911C2×C4—42no—
912C2×C4—42no—
913C2×C4—42no—
914C2×C4—42no—
915C2×C4—42no—
916C2×C4—42no—
917C2×C4—82no—
918C2×C4C23×#12011yescharacteristic
919C2×C4C23×#12011yescharacteristic
920C2×C4C23×#12011yescharacteristic
921C2×C4C23×#12011yescharacteristic
922C2×C4C23×#12011yescharacteristic
923C2×C4C23×#12011yescharacteristic
924C2×C4C23×#12011yescharacteristic
925C2×C4C23×#12011yescharacteristic
926C2×C4C23×#12011yescharacteristic
927C2×C4C23×#12011yescharacteristic
928C2×C4C23×#12111yescharacteristic
929C2×C4C23×#12111yescharacteristic
930C2×C4C23×#12111yescharacteristic
931C2×C4C23×#12111yescharacteristic
932C2×C4C23×#12111yescharacteristic
933C2×C4C23×#12111yescharacteristic
934C2×C4C23×#12111yescharacteristic
935C2×C4C23×#12111yescharacteristic
936C2×C4C23×#12111yescharacteristic
937C2×C4C23×#12111yescharacteristic
938C2×C4C23×#12711yescharacteristic
939C2×C4C23×#12711yescharacteristic
940C2×C4C22×D4×C2311yescharacteristic
941C2×C4C22×D4×C2311yescharacteristic
942C2×C4C22×D4×C2311yescharacteristic
943C2×C4C22×D4×C2311yescharacteristic
944C2×C4C22×D4×C2311yescharacteristic
945C2×C4C2×#41×C2311yescharacteristic
946C8—24no—
947C8—24no—
948C22—22no—
949C22—22no—
950C22—22no—
951C22—41no—
952C22—41no—
953C22—41no—
954C22—41no—
955C22—44no—
956C22—48no—
957C22—42no—
958C22—42no—
959C22—44no—
960C22—82no—
961C22—84no—
962C22—82no—
963C22—84no—
964C22—84no—
965C22—84no—
966C22—84no—
967C22—82no—
968C22—84no—
969C22—82no—
970C22—82no—
971C22C23×#39211yescharacteristic
972C22C23×#39211yescharacteristic
973C22C23×#39211yescharacteristic
974C22C23×#39211yescharacteristic
975C22C2×C23×#12011yescharacteristic
976C22C2×C23×#12111yescharacteristic
977C22C2×C23×#12711yescharacteristic
978C4—44no—
979C4—42no—
980C4—42no—
981C4—82no—
982C4C23×#39211yescharacteristic
983C4C23×#39211yescharacteristic
984C4C23×#39211yescharacteristic
985C4C23×#39211yescharacteristic
986C4C2×C23×#12011yescharacteristic
987C4C2×C23×#12011yescharacteristic
988C4C2×C23×#12111yescharacteristic
989C4C2×C23×#12111yescharacteristic
990C2—21no—
991C2—21no—
992C2—21no—
993C2—21no—
994C2—21no—
995C2—21no—
996C2—84no—
997C2—82no—
998C2—82no—
999C2C23×#200812yesdirect product factor
1000C2C2×C23×#39211yescharacteristic
subgroupG/H
center, socleC22×C23#392
commutator, Frattini, cosocleC22×C4C24×C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C23 ◁ C23×C4×C23 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C23×#575C2semidirect
2. C22×C23×AGL(1,ℤ/8)C2semidirect
3. C2×C23×#535C2semidirect
4. C2×C23×#421C2semidirect
5. C2×C23×#418C2semidirect
6. C2×C23×#410C2semidirect
7. C23×#2008C2direct (N × H)
8. C2×C23×#344C2semidirect
15. C23×#575C22semidirect
25. C2×C23×AGL(1,ℤ/8)C22semidirect
34. C23×#535C22semidirect
42. C23×#421C22semidirect
45. C23×#418C22semidirect
48. C23×#410C22semidirect
50. C23×#344C22semidirect
73. C2×#41×C23D4semidirect
77. C22×Q8×C23D4semidirect
95. C22×D4×C23D4semidirect
131. C2×M16×C23D4semidirect
132. C2×M16×C23D4semidirect
133. C2×M16×C23D4semidirect
137. C22×C8×C23D4semidirect
218. C2×Q8×C23C2×D4semidirect
272. C2×D4×C23C2×D4semidirect
316. M16×C23C2×D4semidirect
322. C2×C8×C23C2×D4semidirect
336. C2×#2008C23direct (N × H)
448. C2×#575C2×C23semidirect
449. C22×AGL(1,ℤ/8)C2×C23semidirect
450. C2×#535C2×C23semidirect
451. C2×#421C2×C23semidirect
452. C2×#418C2×C23semidirect
453. C2×#410C2×C23semidirect
454. #2008C2×C23direct (N × H)
455. C2×#344C2×C23semidirect
504. #575C22×C23semidirect
514. C2×AGL(1,ℤ/8)C22×C23semidirect
523. #535C22×C23semidirect
531. #421C22×C23semidirect
534. #418C22×C23semidirect
537. #410C22×C23semidirect
539. #344C22×C23semidirect
549. C2×C23#2008direct (N × H)
573. C2×#41D4×C23semidirect
577. C22×Q8D4×C23semidirect
595. C22×D4D4×C23semidirect
631. C2×M16D4×C23semidirect
632. C2×M16D4×C23semidirect
633. C2×M16D4×C23semidirect
637. C22×C8D4×C23semidirect
664. C23C2×#2008direct (N × H)
719. C2×Q8C2×D4×C23semidirect
773. C2×D4C2×D4×C23semidirect
817. M16C2×D4×C23semidirect
823. C2×C8C2×D4×C23semidirect
999. C2C23×#2008direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C23×#5752
C22×C23×AGL(1,ℤ/8)2
C2×C23×#5352
C2×C23×#4212
C2×C23×#4182
C2×C23×#4102
C23×#20082
C2×C23×#3442
C2×#200823